Nonconvex nonsmooth optimization for bioinformatics
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Authors
Shabbeer, Amina
Issue Date
2013-12
Type
Electronic thesis
Thesis
Thesis
Language
ENG
Keywords
Computer science
Alternative Title
Abstract
Generating such a graph embedding involves addressing two challenges (i) preserve proximity relations as measured by some embedding objective, and (ii) simultaneous optimization of an aesthetic criterion, no edge-crossings in the embedding, to create a clear representation of the underlying graph structure. We propose a new approach to generating such an embedding that optimizes for multiple criteria. The method uses the theorems of the alternative to express the condition for no edge-crossings as a system of nonlinear inequality constraints. This approach has an intuitive geometric interpretation closely related to support vector machine classication. While edge crossing minimization can be utilized in conjunction with any optimization based embedding objective, here we demonstrate the approach on multidimensional scaling by modifying the stress majorization algorithm to include penalties for edge crossings. We use an alternating approach to solve this nonconvex problem, iteratively performing two steps: computing the layout for a given set of constraints, and altering the constraints based on the new embedding. We provide a detailed analysis of the convergence of this algorithm. Alternating Directions of Multiplier Methods (ADMM) are proposed as a method for efficiently handling a large number of non-smooth constraints. MAA+, an iterative solution using ADMM is described for generating graph embeddings that adhere to non-intersection constraints between edges. We create spoligoforests generated for all strains of TB observed in patients diagnosed with TB in the U.S. from 2006 to 2010. We also developed a standalone tool for drawing spoligoforests. The method is also demonstrated on a suite of randomly generated graphs with corresponding Euclidean distances that have planar embeddings with high stress.
Description
December 2013
School of Science
School of Science
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY